Some frequent/world travelers here recommend a passport so they're ready to go; others recommend one for peace of mind. Both are good advice.
But, I guess MANY thousands of US citizens cruise the Bahamas/Caribbean daily without a passport. It is true that if you need to unexpectedly fly back to the US for whatever reason you will need a passport.
So, two options: Spend the money, get one now, consider it peace of mind insurance. Or, take your birth certificate and government ID, and you will almost certainly be fine. If you do have some emergency come up, the US embassy can issue "emergency passports." For example, the US Embassy in The Bahamas states they will issue one in 30 minutes during normal business hours, or 24 hours a day emergency passports for genuine emergencies.
Both options work. Getting one now when you don't need it is kind of like paying for insurance; on the small chance you need one you avoid the higher expense and minor hassle of going to the embassy to get one.